In order to develop constraint-preconditioned Krylov methods for (REF ), we specialize the basis-generation processes underlying those methods.
We focus on the [1]} and [2]} processes, which compute orthonormal bases of Krylov spaces associated with symmetric and general matrices, respectively.
For reference, the preconditioned Lanczos process is stated as alg:prec-lanczos in sec:processes.
The standard Lanczos process follows by setting the preconditioner to the identity.
It is straighforward to apply our arguments to the [1]} biorthogonalization process and its transpose-free variants [4]}, [5]}.
We implicitly assume that \(A = A^T\)  when considering the Lanczos process.
